The kinematics of NR scattering is shown in Fig. REF  for a few nuclei. For each isotope, the region to the left of the corresponding solid curve represents allowed values of \(E_R\) , given the IDM mass splitting \(\delta \) . The shape of these curves is determined by the DM velocity distribution. Focusing first on xenon experiments (solid green line), the limitation is twofold: 1) the Xe atomic mass limits the maximum transfer as in Eq. (REF ). 2) The analyzed recoil energy, shown here for XENON1T as a dashed blue line, is restricted in most xenon experiments. For the recoil energy range of \(1-40\)  keV the maximum mass splitting that can be constrained is thus around 250 keV. Recently, XENON1T reported the event spectrum up to the electron recoil energies of 210 keV [1]}. A dedicated analysis of nuclear recoils at high energy would be required to constrain mass splitting above 200 keV, but the sensitivity will still be limited to \(\delta <450\)  keV due to the limited mass number of Xe isotopes. Conversely, tungsten (solid grey line) is a heavy and stable element, well-suited to exploring high mass splittings. CRESST-II (CaWO\(_4\) , dashed grey line) analyzed recoil data up to 120 keV, which translates to a mass splitting of about 420 keV. Although the CRESST-III [2]} data are also available, the detector was optimized to sub-GeV mass dark matter detection with better performance at low recoil energies. Therefore, we still expect CRESST-II to set the leading bound at higher mass splittings.
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